Multiple choice

Some amount of acid is taken out of a 54 L vessel full of acid and then, an equal amount of water is added to it. The process is repeated once more. As a result, the vessel now contains 24 L pure acid. How much acid was taken out initially?

  1. 15 L

  2. 16 L

  3. 18 L

  4. 24 L

  5. 20 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount taken out. After two replacements, the remaining acid is 54 * (1 - x/54)^2 = 24. (1 - x/54)^2 = 24/54 = 4/9. 1 - x/54 = 2/3. x/54 = 1/3. x = 18.

AI explanation

Using the replacement formula, Final Amount equals Initial Amount multiplied by the fraction of liquid remaining, raised to the number of repetitions. We have 24 equals 54 multiplied by (1 minus x divided by 54) squared. Solving (1 minus x divided by 54) equals two thirds gives x divided by 54 as one third, making the initially removed acid 18 L.

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